This is also a pet peeve of mine, but I think an even more compelling argument is simply to look at how long people lived in the past. For instance, just among the Founding Fathers - John Adams lived to 90, Sam Adams to 81, Ben Franklin to 84, John Jay to 83, Thomas Jefferson to 83, James Madison to 85. The only person that didn't make it to their 50s, Alexander Hamilton, was killed in a duel (by the current vice president, at the time, no less).
Most people know about low life expectancies in the past, but then extrapolate that to your expected age of age of death, but that's completely wrong. Low life expectancies were owing almost entirely to extremely high rates of infant mortality. If one guy lives to 80, and another dies shortly after birth - you now have a life expectancy of 40 years. The peaks of human longevity don't seem to have changed much, if at all, for millennia.
More people are able to hit those peaks, but that's generally owing to pretty simple advancements like antibiotics, as well as doing away with what were probably overtly harmful treatments. For instance George Washington died relatively young at 67. And while there is some debate on the exact cause, there's reason to believe that his treatment contributed to it. He was being leeched, which was supposed to balance out the 4 humors of the body by drawing out 'bad blood.' And people were reaching the same heights of longevity in the context of that being the bleeding edge of medicine.